ATLAS Algebra II Functions Practice

Functions skills

Understand the concept of a function and use function notation

Interpret functions that arise in applications in terms of the context

Analyze functions using different representations

Build new functions from existing functions

Construct and compare linear, quadratic, and exponential models and solve problems

Interpret expressions for functions in terms of the situation they model

Standards basis

Arkansas Academic Standards for Mathematics (CCSS-M–aligned / Arkansas-adopted math standards) — Arkansas

How the ATLAS reports it

Arkansas’s statewide assessment system is ATLAS, which the ADE page says began serving in spring 2024. The official public page does not publish a math blueprint there, so the most defensible coverage map is the Arkansas math standards structure that ATLAS is aligned to.

Blueprint & weighting

ATLAS uses the Independent / state-specific framework (by grade domains structure).

Official sources

Arkansas DESE Assessment: Test Scores
Arkansas DESE home page
Arkansas DESE: 3–10 ATLAS Content Assessments

8 free questions · 0/0 correct

Practice playeasy

The function $f$ is defined by $f(x) = 3x^{2} + 2$ . What is the value of $f(x)$ when $x = 2$ ?

Substitute $x = 2$ : $f(2) = 3(2)^{2} + 2 = 3(4) + 2 = 12 + 2 = 14$ .

Practice playeasy

The function $f(x)$ is defined by $f(x) = -3x + 20$ . For what value of $x$ does $f(x) = 5$ ?

Set $-3x + 20 = 5$ . Then $-3x = -15$ , so $x = 5$ .

Practice playeasy

For the function $h$ , $h(0) = 64$ . For each increase in $x$ by $1$ , the value of $h(x)$ decreases by $25\%$ . What is the value of $h(2)$ ?

Each step multiplies by $1 - 0.25 = 0.75$ . So $h(2) = 64 \cdot 0.75^2 = 64 \cdot 0.5625 = 36$ .

Practice playeasy

$a = 250 + 15w$

The equation shown gives the estimated balance $a\textsf{,}$ in dollars, in a savings account after $w$ weeks of deposits, where $0 \le w \le 20\textsf{.}$ What is the estimated balance, in dollars, in the savings account after $6$ weeks of deposits?

Substitute $w = 6\textsf{:}$ $a = 250 + 15(6) = 250 + 90 = 340\textsf{.}$ The estimated balance is $340$ dollars.

Practice playeasy

What is the value of $\log_{2}16\textsf{?}$

$2^{4} = 16\textsf{,}$ so $\log_{2}16 = 4\textsf{.}$

Practice playeasy

An $80$ -milligram sample of a radioactive isotope has a half-life of $4$ years.

Choose the function model that correctly calculates the amount remaining after $12$ years.

The remaining amount after $t$ years is $A(t) = 80\left(\dfrac{1}{2}\right)^{\textstyle\frac{t}{h}}\textsf{,}$ where $h$ is the half-life. Here $t = 12$ and $h = 4\textsf{,}$ so $A(12) = 80\left(\dfrac{1}{2}\right)^{\textstyle\frac{12}{4}} = 80\left(\dfrac{1}{2}\right)^{3} = 10\textsf{.}$

Practice playeasy

The function $g$ is defined by $g(t) = 840(0.5)^{t/4}$ . The function $g$ models the mass, in milligrams, of a medicine in a patient's bloodstream, where $t$ is the number of hours after an injection. According to the model, what is the estimated mass, in milligrams, of the medicine at the time of the injection?

At the time of injection, $t = 0$ . So $g(0) = 840(0.5)^0 = 840$ milligrams.

Practice playeasy

You invest $\text{\char36}100$ at $10\%$ annual interest compounded yearly for $2$ years. What is the total?

Year 1: $100 \times 1.10 = 110$ . Year 2: $110 \times 1.10 = 121$ .

ATLAS Algebra II Functions. Practice it free.

Functions skills

Understand the concept of a function and use function notation

Interpret functions that arise in applications in terms of the context

Analyze functions using different representations

Build new functions from existing functions

Construct and compare linear, quadratic, and exponential models and solve problems

Interpret expressions for functions in terms of the situation they model

Topics mapped to this domain

Evaluating functions

Evaluating functions at a value

Evaluating functions from percent change

Evaluating functions in context

Evaluating logarithms (ACT)

Exponential functions

Exponential functions in context (SAT)

Exponential and log formulas

Factored polynomial x-intercepts (SAT)

Intercepts from general form

Interpreting function values in context

Linear functions from tables (ACT/SAT)

8 free questions · 0/0 correct

Turn functions into game time.

More Algebra II domains